Graded weakly 1-absorbing prime ideals

Author
Tekir, Ünsal

Koç, Suat

Abu-Dawwas, Rashid

Yıldız, Eda

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https://revistas.ufro.cl/ojs/index.php/cubo/article/view/3103
10.56754/0719-0646.2402.0291
Abstract
In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let \(G\) be a group and \(R\) be a \(G\)-graded commutative ring with a nonzero identity \(1\neq0\). A proper graded ideal \(P\) of \(R\) is called a graded weakly 1-absorbing prime ideal if for each nonunits \(x,y,z\in h(R)\) with \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.
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